Thanks! And thanks for following the series.
These are great questions. I'll try to take them in turn:
1. I have indeed seen some excellent modeling of the distributional impacts of a cap and dividend proposal, which you can find from James Boyce and Matthew Riddle at UMass Amherst here. They model net impacts on households on each income decile and in each state and find "at least 60% of households receive net benefits: the dividends more than offset the impact of higher fossil fuel prices on their real incomes." So your intuition seems spot on. A equal per capita carbon dividend would be a progressive income shift.
Dallas Burtraw and colleagues at Resources for the Future modelled the distributional impacts of a variety of uses of revenues from a cap and trade program on the U.S. electricity sector only, which you may find helpful on this topic as well.
A tax shift (i.e. income tax cut) would be less directly progressive, as unless it is fully refundable, it would miss out on low-income non-tax payers, although for those it would benefit, it would be progressive if it was enacted as a tax cut in equal dollar terms for each income bracket. So a tax shift might end up more benefiting the middle class over lower incomes unless designed with some kind of low income payments or if tax credits were fully refundable. Note though that most real-world tax shift proposals I've seen (including BC's, Australia's now-dead tax, and the failed Canadian Green Shift) all include business income tax cuts as well to offset impacts to business and industry. That would make the tax less progressive overall, as business owners and shareholders tend to be higher income.
2 & 3. If an effective public education campaign convinced a majority of Americans that they would end up ahead because of a cap/tax and dividend scheme, I'm sure it would increase public support versus a cap/tax with non-earmarked use of funds. That said, there are three things to consider: First, the gains for individuals would be minor and diffuse. Are citizens really going to want to see a carbon tax that forces changes in their behavior so that they can earn an extra $50 or $150 per household per year? Will they trust that the government is really going to give them their money back? If they can save another $50 by changing their habits, will they see that as a positive, or will they question why they are being forced to change their habits in the first place? I'm sure there's going to be a fair amount of skepticism to that proposal, even if the math works out in their favor on an annual basis. Second, the wealthier income brackets lose out, and it's sad to say, but in our current American version of "democracy," these income brackets have a disproportional impact on politics. Third, a real per capita dividend approach does nothing to blunt impacts on industry (all the revenues go to households as dividends). So the political economy constraints arising from industries with high asset specificity (as discussed in Part 1) will be fully unleashed in opposition to any cap/tax and dividend proposal.
So in sum, I think using revenues for dividends increases somewhat the level of carbon price that is politically sustainable. But how far? Certainly the use of dividends does not free carbon pricing from political economy constraints! Far from it. So let's be optimistic and say that it doubles the public willingnes to pay for carbon pricing: so if we can see a WTP equivalent to a $2-8/ton of CO2 tax without dividends, then maybe we can increase that to $4-16/ton CO2. But the dividends do nothing to blunt industry opposition to the tax. Those constraints will surely further limit if not outright prevent the carbon price. So where do these dividends leave us? My contention is that we'd still end up with a potentially feasible carbon tax that is far below the social cost of carbon. What do you think?
4. I think that if you could get it implemented, the dividends would probably make the carbon tax more durable over time. Maybe. Then again, getting rid of the tax entirely would always have some appeal.
5. I think that there would be three keys to a politically sustainable tax and invest scheme: 1. keep the carbon tax low in the first place. A $5 per ton carbon tax would raise about $25 billion per year in the U.S. for example, but raise the cost of a gallon of gasoline by only about 5 cents and would have a very negligible impact on electricity prices. A modest tax is much less likely to become the focus of public ire. 2. Structure RD&D programs wisely. See the links in my comment to Joris below on how to do that, to minimize the changes of a major 'debacle' like Solyndra. And 3. invest in a way that really drives down the cost of clean energy over time. That reduces the "lift" that the carbon price itself has to accomplish and thus helps ensure the tax and stay low while finishing the job on the Co2 reduction side. All in all, I'm pretty confident you could make something like that work. What do you think?